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Proof step 3 from proof ac-init-09 (previous step)

⊦ initerror(class1, addclass(class1, fis + (mkfs(class1, void_type, `initstate' .field) ' × val) ', st)) ↔ val = initval(error), mkfs(class1, void_type, `initstate' .field) ' ∈ fis

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ initerror(class1, st) ↔ (jvmref -- mkfs(class1, void_type, `initstate' .field) ') × initval(error) ∈ st
Proof step 2:
mkfs(class1, ty, fieldvar) ' ∈ fis ⊦ (jvmref -- mkfs(class1, ty, fieldvar) ') × val ∈ addclass(class1, fis, st) ↔ fis[mkfs(class1, ty, fieldvar) '] = val

Rule argument

[speclemmaarg: , initerror(class1, st) ↔ (jvmref -- mkfs(class1, void_type, `initstate' .field) ') × initval(error) ∈ st ,[st, class1] → [addclass (class1, fis + (mkfs(class1, void_type, `initstate' .field) ' × val) ', st), class1] ,F ,storefuns , ,initerror ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ sk ∈ fis + (sk × val) '], [CSIMPSEQ : ⊦ ¬ sk ∈ fis → (fis + (sk × val) ')[sk] = val], [CSIMPSEQ : ⊦ initval(istate) = initval(istate0) ↔ istate = istate0])], [EXTRATERMS : (addclass (class1, fis + ( mkfs(class1, void_type, `initstate' .field) ' × val ) ', st), class1)]]